Generalized factorization theory for integral domains was initiated by D. D. Anderson
and A. Frazier in 2011 and has received considerable attention in recent
years. There has been significant progress made in studying the relation
for the integers in previous undergraduate and graduate research projects.
In 2013, the second author extended the general theory of factorization to
commutative rings with zero-divisors. In this paper, we consider the same relation
over the modular
integers,
.
We are particularly interested in which choices of
yield a ring which satisfies
the various
-atomicity
properties. In certain circumstances, we are able to say more about these
-finite factorization
properties of
.